%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET849-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:31:09 AM UTC 2026
% Result : Unsatisfiable 5.05s 3.06s
% Output : Refutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 130 ( 6 ~; 4 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Zorn_Osucc_decl,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Zorn_OTFin_decl,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(1,negated_conjecture,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(5,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ ( v_S @ c_Zorn_Osucc ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(8,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ tc_set @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ tc_set @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) )
= ( B @ ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) @ ( A @ c_Zorn_Osucc ) ) ) )
| ~ ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) )
= ( B @ ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) @ ( A @ c_Zorn_Osucc ) ) ) )
| ~ ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ ( B @ tc_set @ ( B @ ( A @ c_Zorn_OTFin ) @ c_Union ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[5,8,9,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET849-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n020.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 08:22:19 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.33/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.76/1.46 % [INFO] Parsing done (265ms).
% 1.76/1.48 % [INFO] Running in sequential loop mode.
% 2.79/2.10 % [INFO] eprover registered as external prover.
% 2.79/2.12 % [INFO] Scanning for conjecture ...
% 3.08/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 3.08/2.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 3.24/2.32 % [INFO] Problem is propositional (TPTP CNF).
% 3.24/2.33 % [INFO] Type checking passed.
% 3.24/2.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.58/3.06 % External prover 'e' found a proof!
% 4.58/3.06 % [INFO] Killing All external provers ...
% 5.05/3.06 % Time passed: 2441ms (effective reasoning time: 1569ms)
% 5.05/3.06 % Axioms used in derivation (3): cls_Set_Osubset__refl_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_Oequal__succ__Union_1
% 5.05/3.06 % No. of inferences in proof: 9
% 5.05/3.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2441 ms resp. 1569 ms w/o parsing
% 5.05/3.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.05/3.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------